What does this problem mean?

I received a great question this morning about a math problem from Bits and Pieces 2:

Can you give me an example on how to find two fractions with a sum that is between the two given numbers? [ex:] #20. 0 and 1/2.

I like this question because it is completely unlike how I was taught how to learn and do math in middle school. It made me think about how much more in-depth this kind of math question is. Here is my reply. 

... mostly, these kinds of questions in the books are thinking exercises and not calculation exercises.

This first lesson doesn’t focus on exact methods of solving the problem. It is focusing the kids on thinking about the benchmark fractions that they know “by heart.” It is asking them to reason things out without needing to come up with a specific answer (estimation skills). A typical way of thinking about it might go like this [imagine a student thinking it to themselves]:

I know what 1/2 is. I know that 1/2 is the same as 1/4 + 1/4. So since 1/4 + 1/4 is too big for the problem (because they equal 1/2 exactly), I need to use a fraction that is smaller than 1/4. Any fraction smaller than 1/4. I'll try half of a quarter: 1/8. So 1/8 + 1/4 has to be less than 1/2 but it will still be more than 0.

No need for an exact answer to the problem, the students know from their benchmark values that the sum must be less than 1/2 but more than 0, so 1/8 + 1/4 meets those criteria.

This kind of open ended question provides the kids practice with algebraic reasoning. It sets the students up to be much more independent mathematical thinkers so that they can reason about their math class instead of just memorizing steps.

Of course, the chosen fraction could have been anything smaller than 1/4. But I thought this was a great example to illustrate what these "thinking" questions are trying to get the students to do and how they might approach it.

WMS: EdVenture Team: Request for a change in supplies: Please bring a composition book for math.

Dear parents and families,

We have had a busy week so far getting ready for student-led conferences, selecting work samples to share, and still making progress on our math curriculum. While helping students prepare for conferences, it has become very clear to me that many many students need some help with organizing their math work and so I have a request of you.

The short version of my request:

After Thanksgiving break, I would like to start using composition books for our math work. If you are able, please send a composition book with your child to school any time between now and the first day after thanksgiving break. The composition book will travel with your child between school and home and will serve as a single place for all math-related materials and work.

The long version of my request:

This fall there was a mysterious item on the school shopping list: a spiral bound graph paper notebook. I say it was a mystery because Mr. Knickrehm didn't know what it was for and it was very difficult to find one (most people couldn't find one). Well, I was talking with Amy Berreth (who just this year switched to seventh grade math) and she told me all about it. It turns out she used this as a single place for her students to do all their work and keep all of their papers. Amy's system used the notebook -- kind of like a science notebook -- as a place for students to do all their work and to archive all of their assessments. It was easy for her and parents to gauge a child's progress on a daily basis because at the end of each and every work period, they drew a straight line and put the date and time on it. Ah-ha! Immediately I understood why she used this system.

This year I am learning to help students strive for excellence in a self-paced manner through a very neat curriculum. But in order to self-pace the materials, there are lots of extra pieces of paper to help a student navigate through them. I have been trying to find ways of helping students keep all of these various papers organized (roadmaps, flash feedbacks, target practices, lab sheets). And it's been very difficult for most students to keep track of all their papers in the binders because things get torn accidentally and fall out. I have given a composition book to a few students already to help with organization and it usually has worked out well for them. I would like very much to begin using Amy's system as soon as possible with all of my students. But I would like students to use a composition book (the stiff-backed ones with either graph paper or lined paper inside).

I realize that at this time of year, composition books are not at their cheapest price. I think they range anywhere from $2.50 to $4.00 right about now. If this is a burden that you cannot float right now, please let me know. I have a few composition books left from when I was an eighth grade science teacher and I can give one to your child kind of like a scholarship.

Thank you for all you do to support your children and their school.

Sincerely,

Brian

WMS: EdVenture Team: BNYC Tutoring Available!

The Broadway Neighborhood Youth Center (BNYC) wants you to know that they have a group of WWU students that are interested in tutoring. They will be offering this in Whatcom's portables on F Street.

If you would like to take advantage of the tutoring for your child, please call the BNYC @ 933-1021. You will need to commit to a definite day and time.

Cheers,

Brian MacNevin

Bully-Proofing

Today and for the next three Mondays, our school counselor, Beth Schille, will be coming into my classroom to teach our EdVenture Team students the Bully-Proofing lessons for our school. If you have any questions about the curriculum, the lessons, or things that you have heard about it from your students, please do not hesitate to contact Beth [link] and ask directly.

Mr. Knickrehm and I believe these lessons are so important for the culture of Whatcom Middle School. At this time in students' lives, they need to know how to navigate not just interpersonal relationships, but how to advocate for others who don't advocate for themselves or who don't have a peer group to advocate for them. This curriculum and the discussions around it help students to think about their role in bullying situations they may be a part of or that they may merely be witnessing.

Thank you for supporting your child's self-reflection on bullying in schools.

Peace.

Quiz this Friday: 10/21/2011

We have our first quiz this Friday, 10/21/2011.

Here is a link to some practice problems. The practice problems come from two segments of Investigation 2 in our curriculum.

Investigation 2 Quiz Practice Problems

Some students are still finishing up their Investigation 2 work this week, but they should be done by Thursday.

30 minutes of math homework... EVERY night.

I just wanted to update families on homework for math. I have heard from several parents over the last week that their child claims s/he has no math homework because it was finished in school. This is incorrect. Students should spend 30 minutes every night working on math (Monday through Thursday).

What can they do during those 30 minutes?

1. Review the day's Math Review.
2. Practice any Math Review questions that were incorrect.
3. Work on the next Problem, the next ACE set, or the next Target Practice on the road map.
4. Practice those multiplication and division facts!

So any time your child claims that s/he finished her/his homework at school, you can confidently say, "you may have finished your ACE questions, but you have way more you could work on."

Thanks for all you do to support your child!

Mr. Mac

The Structure of a Math Period... and Homework

Structures...
I wanted to take a moment to describe for families the general structure of a math period with me. Usually we have about 70 to 80 minutes of time for math. During that time we'll go through these activities:

• Math Review
• On Mondays and Wednesdays we take 10 minutes to do four review math problems. Then we take about 10 minutes to go over the answers and to share strategies.
• On Mondays and Wednesdays they also take a new math review home to do as homework. 
• On Tuesdays and Thursdays we start the day by going over answers to these math reviews. 
• As we are going over answers, students are responsible for recording what they get right and what they get wrong and for recording strategies that they didn't use or writing notes about what they got wrong and how to fix it. 
• On Fridays we have a four question quiz covering problems similar to the ones that were on that week's math reviews.
• Check-in Time
• I check in to see what students are working on right now.
• Math Workshop
• This is self-paced time. Students work on the assignments on their roadmaps, they self-correct using answer keys, they should go back and correctly solve anything incorrect, they work on mini quizzes.
• Students may work with a partner on any problems and/or ACE questions. But each student must write down his or her own work.
• "Target Practice" assignments and "Flash Feedbacks" (the mini quizzes) must be done individually.
• Check-up Time
• Students tell me what they're working on right now and what they will do as homework that night.

30 Minutes of Math Each Night!

Homework is a little different in this kind of structure. 6th grade students are expected to have 60 minutes of homework a night. I expect 30 minutes to be spent on math.

• Every Monday and Wednesday night:
• Students should review that day's math review at home. Anything they got incorrect they should try again at home. This might mean practicing calculations, memorizing vocabulary, or reworking story problems.
• Students will have a new 4-question math review. They need to do all four problems.
• Monday, Tuesday, Wednesday, and Thursday nights:
• During Check-up time, students tell me what they will work on that night for homework. Essentially, they must spend time getting farther on their current roadmap. 
• Occasionally students will be at a point where there is nothing to work on (these are called Flash Feedbacks and they are done only in class). In that case, they should look for "ACE" questions in the book that they haven't done yet and should choose some to work on. 
• Fridays
• Fridays are usually homework-free days. But sometimes there will be an exception.